Logistic optimization with Monte Carlo based system models

It is by now clear that reliable design models for large and complex industrial and systems must be based on Monte Carlo (MC) calculations. Such models involve aging of LRUs (Line replaceable units) and interactions between various LRUs and subsystems that can not be presented and solved by analytic methods. A logistic model involves both the systems and the "Logistic Envelope" designed to sustain the operation of the system. This includes spare parts at various sites, repair and diagnostics sites, repair teams and repair and maintenance equipment. The optimization of the logistic envelope is critical to the effectiveness of the system. Such optimization requires two basic elements - First a description of the performance (Availability, production etc.) as function of the logistic parameters - Spare parts in every location, number of repair teams etc. and a search method in this multidimensional space that will enable locating the optimum. Both elements are missing in a Monte Carlo model. One does not have a simple function that represents the performance because of the numerical nature of the calculation and in each known search method hundreds or even thousands MC calculations may be required. Each MC calculation may require several hours or days which makes the optimization virtually impossible. To solve the above problem both elements are addressed: The performance as function of the logistic parameters utilizes a hybrid approach by which an analytic approximation is built with bulk parameters learned from a small number of MC calculation. For the search mechanism we present a new and novel approach based on a new theorem, referred to as the "Central theorem of logistic optimization". These two elements together enable the construction of a rigorous and practical algorithm for optimization. The new method is explained and is verified and validated using two worked out examples. It is also compared with other commonly used methods.